As a nation state, Italy has emerged only in 1871. Until then the country was politically divided into a large number of independant cities, provinces and islands. The currently available evidences point out to a dominant Etruscan, Greek and Roman cultural influence on today's Italians.

I have recently wrote to Ufficio Anagrafe from the Comune di Lucca and in reply they have found the ancestors such as the Brunicardi from my father's mother's side. I am wondering how much does it cost normally for requesting certificato di stato di famiglia storico? I am surprised of how much they want and they don't specify what they have found exactly but it is from the year 1866 to 1909.

Since it has been quite hard to finding any information on father's side, I am quite happy they found any information. As you stated it is a 40 year span which is quite alot. They haven't specified on how many people they found, should they have been more specific on what their charges are or should I take it as what they have stated? They are also charging 14.62 for delivery which leads me to believe there is alot of documents I will be looking at. Since I have never seen what a famiglia storico would look like. Are they photocopied documents or will they just transcribe it in a letter form.

In my research I have learned that each town organizes it's records as it pleases. Some towns have 10 year alphabetical indexes, making it easy to pullout family groups on request. Others keep updating the various census, with families in page form (like James 'anagrafe'). Others have an alphbetical listing of citizens that shows birth, marriage and death details, but to pull out family members requires a lengthy search.
Occasionally when I have requested a search without a date the charge is 5 euro for each certificate, and they won't look for anyone for whom I don't have a name.
Asking for a 3-4 generation search can be very time consuming for the very busy Anagrafe office. It's doubtful they have photocopied the records for you but have likely prepared the official certificates that require a signature and stamp (more time).
Just so you know, the 'anagrafe' is the Italian word for the record-keeping department of the town hall.